My daughter and I went on a 12 week- journey last year to explore Fractions. We are doing it again this Fall. I am updating the posts from last year with videos, in case you want to join us this year. Click here if you want to know more about the journey and the previous problems.
Here is Problem #4, a second measurement division problem.
Level Yellow : Ms. Butternut makes wooden toys. She has 5 wheels. She needs 2 wheels to make a motorcycle. How many motorcycles can she make?
Level Orange : Ms. Butternut makes wooden toys. She has 14 wheels. She needs 4 wheels to make a car. How many cars can she make?
Level Red : Ms. Butternut makes wooden toys. She has 31 wheels. She needs ____ wheels to make a heavy truck. How many heavy trucks can she make?
As always, invite your child to solve one of the problems by
- modeling the problem with manipulatives (such as buttons, marbles, etc, and small containers),
- representing the problem on a piece of paper, and/or
- writing an equation.
With all Levels, Ms Butternut has a left over of wheels. (Level Yellow: 2 motorcycles can be made, with 1 wheel left, Level Orange: 3 cars can be made, with 2 wheels left).
When your child is done, invite him/her to share his/her reasoning with you. By now, you know the routine, right ? :-)
Sharing my experience (Fall 2015)
Last week, my child decided to mostly model with manipulative the problems. I think she was not sure how to represent the problem, and confused with the equation she could use. This week, she seemed more confident in her exploration.
With Level Orange, she started with drawing 14 wheels, and took away groups of 4 one at a time. With such strategy, she quickly saw the equation that could be associated to her reasoning: a repeated subtraction (which is how division can be seen). She used the left over to make a bicycle, but your child may state that Ms Butternut has 2 wheels left.
With Level Red (31wheels, 6 wheels / truck), she decided to draw tallies (by groups of 5) to represent 31 wheels. Then, as previously, she took away groups of 6, to end up with 5 trucks (and a tricycle i.e 3 wheels left). Now, I do not know how she did not get confused with taking groups of 6 out of her tiny groups of 5 tallies, but she did say along the process that “maybe using tallies was not such a good idea”. I enjoyed watching Rosie discover on her own that some representations may work better in some situations, and less in others. Indeed, it is going to be up to her to select the most useful one depending on the problem.
I am also sharing below the work of a friend’s child, a 5th grader solving Level Red. In parallel with writing the equation, and labeling each part of it, the child also explained the model she could use to solve the problem.
Sharing my experience (Fall 2016)
Funny how, from one year to the next, a same problem could lead to another exploration. Last year, Rosie drew all the wheels, and took away groups of them (e.g. a group of 4, while solving Level Orange). This year, she added up the groups of wheels needed for one vehicle (e.g. 6 wheels, like last year, to make a truck) until she reaches the total number of wheels available. Such an interesting way to explore the connections between all operations. Also, I think she enjoyed adding equations afterwards, as she could fully connect every part to the picture.
Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.